A deal thrashed out with the Kremlin-backed energy company in January that envisaged both a share exchange and an Arctic exploration joint venture expires at midnight.

With the clock ticking, BP chief executive Bob Dudley was in "non-stop" talks last night with Rosneft to extend the deadline for the share-swap part of the deal before he faces shareholders at the AGM. Failure to preserve the deal could lead to angry questioning from investors over BP's leadership.

Sources close to the talks said last night that BP was "cautiously optimistic" – though there was no guarantee a deal could be done.

A Rosneft spokesman said earlier in the evening: "We are in consultations at a working level", with sources suggesting it could turn to Royal Dutch Shell or ExxonMobil if the BP talks collapse.

The Rosneft transaction is Mr Dudley's first big strategic move since taking over as chief executive in the wake of last year's devastating Gulf of Mexico oil spill that left 11 dead and the company facing a $40bn bill.

But his repositioning of the company away from America to the east has run into a furious row with BP's existing Russian partner, TNK-BP, half of which is owned by four Russian oligarchs operating as Alfa-Access-Renova (AAR).

The four – Mikhail Fridman, Len Blavatnik, Viktor Vekselberg and German Khan – have used a court to block both the Arctic exploration and share-swap elements of the Rosneft deal, arguing they contravene the TNK-BP shareholder agreement. A bitter dispute reached a fresh impasse on Wednesday when both BP and Rosneft halted talks over a proposed $27bn buy-out of AAR.

Sources close to BP said the UK oil company and Rosneft had made a joint offer to the oligarchs at a "significant premium" to TNK-BP's current market value of $47.5bn.

"They torpedoed those talks by dint of the ludicrous valuation of $70bn they have put on TNK-BP", the source said.

Sources close to AAR denied that, saying: "BP has created this mess and they have not come forward with a credible proposal to sort it out."

Stan Polovets, AAR's chief executive, said: "Our position has always been clear – AAR wanted the entire deal turned over to TNK, not some selected parts." He said BP would "now be sued", with AAR poised to launch a $10bn lawsuit alleging the UK oil giant froze it out of the Rosneft deal.

The stand-off has alarmed investors. One leading shareholder said: "The important thing is for BP not to overpay in resolving the dispute with TNK-BP. We'll be watching carefully for this."

Rather than Mr Dudley, BP chairman Carl Henric-Svanberg is expected to be the lightning rod for shareholder discontent at the AGM – not least because of what some see as his "disappearing act" during last year's spill.

Both men, as well as BP's safety committee chairman Sir William Castell, are among directors standing for re-election. A protest vote is likely.

One top 10 investor said: "The focus of the revolt is Carl-Henric Svanberg, who has not covered himself in glory either during the Gulf of Mexico crisis or since. Dudley is needed at the moment. It's not impossible that Svanberg has to go for a fresh start."